Power pseudovarieties of semigroups. I
For a semigroup S, P(S) denotes the semigroup of all subsets of S, and \(P'(S)=P(S)\setminus \{\emptyset \}\); for a pseudovariety V, PV (P'V) is the pseudovariety generated by all P(S) (P'(S), resp.), \(S\in V\). The main result is a characterization of P'(V) for pseudovarieties V such that every \(S\in V\) satisfies some identity of the form \(x_ 1...x_ kyx_ 1...x_ k=x_ 1...x_ k\).
scientific article; zbMATH DE number 3944149